!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-periodicity-support !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check that the model supports periodic boundary conditions correctly. If the simulation box is increased by an integer factor along a periodic direction, the total energy must multiply by that factor and the forces on atoms that are periodic copies of each other must be the same. The check is performed for a randomly distorted non-periodic face-centered cubic (FCC) cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. For each configuration, all possible combinations of periodic boundary conditions are tested: TFF, FTF, FFT, TTF, TFT, TTF, TTT (where 'T' indicates periodicity along a direction, and 'F' indicates no periodicity). The verification check passes if the energy of all configurations that the model is able to compute support all periodic boundary conditions correctly. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------ Results for KIM Model : EAM_Dynamo_WuTrinkle_2009_CuAg__MO_270337113239_005 Supported species : Ag Cu random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TTT (Configuration in file "config-Ag-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 2.21986669989 2^p V(r_1,...,r_N) = 2.21986669989 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.08598427e+00 -1.13153147e+01 -1.26080567e+01 | -8.08598427e+00 -1.13153147e+01 -1.26080567e+01 1 6.19118944e+00 4.22624172e+00 -4.06070955e+00 | 6.19118944e+00 4.22624172e+00 -4.06070955e+00 2 6.71142241e+00 -5.62194623e+00 7.63812606e+00 | 6.71142241e+00 -5.62194623e+00 7.63812606e+00 3 -4.81662757e+00 1.27110192e+01 9.03064016e+00 | -4.81662757e+00 1.27110192e+01 9.03064016e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TTF (Configuration in file "config-Ag-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 5.20906453452 2^p V(r_1,...,r_N) = 5.20906453452 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.10662607e+01 -7.96444561e+00 -7.16234405e+00 | -1.10662607e+01 -7.96444561e+00 -7.16234405e+00 1 8.40017487e+00 6.49340127e+00 -1.02890337e+01 | 8.40017487e+00 6.49340127e+00 -1.02890337e+01 2 1.23582338e+01 -1.31199695e+01 1.22388203e+01 | 1.23582338e+01 -1.31199695e+01 1.22388203e+01 3 -9.69214795e+00 1.45910138e+01 5.21255751e+00 | -9.69214795e+00 1.45910138e+01 5.21255751e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TFT (Configuration in file "config-Ag-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 8.89893023477 2^p V(r_1,...,r_N) = 8.89893023477 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.05844983e+01 -1.32888218e+01 -1.71028077e+01 | -1.05844983e+01 -1.32888218e+01 -1.71028077e+01 1 1.42575798e+01 1.40511016e+01 -8.41124669e+00 | 1.42575798e+01 1.40511016e+01 -8.41124669e+00 2 9.33679225e+00 -1.23525151e+01 1.29768372e+01 | 9.33679225e+00 -1.23525151e+01 1.29768372e+01 3 -1.30098737e+01 1.15902353e+01 1.25372172e+01 | -1.30098737e+01 1.15902353e+01 1.25372172e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TFF (Configuration in file "config-Ag-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 18.7122437854 2^p V(r_1,...,r_N) = 18.7122437854 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.81426727e+01 -1.74467541e+01 -2.77639882e+01 | -1.81426727e+01 -1.74467541e+01 -2.77639882e+01 1 1.22136626e+01 1.43916606e+01 -9.87526882e+00 | 1.22136626e+01 1.43916606e+01 -9.87526882e+00 2 2.19904023e+01 -1.54037514e+01 2.23963978e+01 | 2.19904023e+01 -1.54037514e+01 2.23963978e+01 3 -1.60613922e+01 1.84588449e+01 1.52428593e+01 | -1.60613922e+01 1.84588449e+01 1.52428593e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = FTT (Configuration in file "config-Ag-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 8.41641266548 2^p V(r_1,...,r_N) = 8.41641266548 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.44392646e+01 -1.04501039e+01 -1.36990258e+01 | -1.44392646e+01 -1.04501039e+01 -1.36990258e+01 1 1.03517131e+01 1.27215472e+01 -1.10439009e+01 | 1.03517131e+01 1.27215472e+01 -1.10439009e+01 2 1.36451579e+01 -1.44105446e+01 1.23977098e+01 | 1.36451579e+01 -1.44105446e+01 1.23977098e+01 3 -9.55760648e+00 1.21391013e+01 1.23452169e+01 | -9.55760648e+00 1.21391013e+01 1.23452169e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = FTF (Configuration in file "config-Ag-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 2.41969381829 2^p V(r_1,...,r_N) = 2.41969381829 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.15257070e+01 -9.99451844e+00 -7.43384220e+00 | -1.15257070e+01 -9.99451844e+00 -7.43384220e+00 1 7.13879159e+00 9.64733947e+00 -8.25833946e+00 | 7.13879159e+00 9.64733947e+00 -8.25833946e+00 2 8.89320625e+00 -4.97542582e+00 1.22038452e+01 | 8.89320625e+00 -4.97542582e+00 1.22038452e+01 3 -4.50629084e+00 5.32260479e+00 3.48833648e+00 | -4.50629084e+00 5.32260479e+00 3.48833648e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = FFT (Configuration in file "config-Ag-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 16.0385582747 2^p V(r_1,...,r_N) = 16.0385582747 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.17295477e+01 -1.08656844e+01 -1.48680656e+01 | -1.17295477e+01 -1.08656844e+01 -1.48680656e+01 1 1.52182918e+01 1.41803812e+01 -1.19795840e+01 | 1.52182918e+01 1.41803812e+01 -1.19795840e+01 2 1.94458336e+01 -2.32501730e+01 1.63653155e+01 | 1.94458336e+01 -2.32501730e+01 1.63653155e+01 3 -2.29345777e+01 1.99354762e+01 1.04823341e+01 | -2.29345777e+01 1.99354762e+01 1.04823341e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTT (Configuration in file "config-Cu-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -6.09086420611 2^p V(r_1,...,r_N) = -6.09086420611 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -3.63877633e+00 -1.46944829e+00 -4.22123414e+00 | -3.63877633e+00 -1.46944829e+00 -4.22123414e+00 1 9.74284629e-01 2.46396245e+00 -1.75840756e+00 | 9.74284629e-01 2.46396245e+00 -1.75840756e+00 2 5.37935512e+00 -3.91702159e+00 4.62376356e+00 | 5.37935512e+00 -3.91702159e+00 4.62376356e+00 3 -2.71486342e+00 2.92250743e+00 1.35587815e+00 | -2.71486342e+00 2.92250743e+00 1.35587815e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TTF (Configuration in file "config-Cu-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -5.51469561376 2^p V(r_1,...,r_N) = -5.51469561376 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.81741202e+00 -1.69049937e+00 -1.96756136e+00 | -2.81741202e+00 -1.69049937e+00 -1.96756136e+00 1 1.69598190e+00 3.28948576e+00 -2.48433485e+00 | 1.69598190e+00 3.28948576e+00 -2.48433485e+00 2 6.99662421e+00 -6.46953234e+00 3.29209735e+00 | 6.99662421e+00 -6.46953234e+00 3.29209735e+00 3 -5.87519409e+00 4.87054595e+00 1.15979885e+00 | -5.87519409e+00 4.87054595e+00 1.15979885e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFT (Configuration in file "config-Cu-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.00988769784 2^p V(r_1,...,r_N) = -7.00988769784 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -3.90836527e-01 -7.09578889e-01 -5.22524801e-01 | -3.90836527e-01 -7.09578889e-01 -5.22524801e-01 1 3.22092799e-01 2.10271305e+00 -3.49010356e+00 | 3.22092799e-01 2.10271305e+00 -3.49010356e+00 2 1.26071115e+00 -3.06071342e+00 3.56269878e+00 | 1.26071115e+00 -3.06071342e+00 3.56269878e+00 3 -1.19196742e+00 1.66757926e+00 4.49929577e-01 | -1.19196742e+00 1.66757926e+00 4.49929577e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = TFF (Configuration in file "config-Cu-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.97565287433 2^p V(r_1,...,r_N) = -3.97565287433 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.03302952e+01 -4.85410213e+00 -1.10195853e+01 | -1.03302952e+01 -4.85410213e+00 -1.10195853e+01 1 2.67513052e+00 4.02528395e+00 -2.56373644e+00 | 2.67513052e+00 4.02528395e+00 -2.56373644e+00 2 1.08296137e+01 -3.22790253e+00 1.07054941e+01 | 1.08296137e+01 -3.22790253e+00 1.07054941e+01 3 -3.17444905e+00 4.05672071e+00 2.87782769e+00 | -3.17444905e+00 4.05672071e+00 2.87782769e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTT (Configuration in file "config-Cu-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.38104806267 2^p V(r_1,...,r_N) = -7.38104806267 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -9.87185782e-01 -7.40991957e-01 1.65197951e-01 | -9.87185782e-01 -7.40991957e-01 1.65197951e-01 1 7.61286203e-01 7.10300604e-01 3.91327684e-01 | 7.61286203e-01 7.10300604e-01 3.91327684e-01 2 -3.38644687e-01 8.28353479e-01 -3.69337398e-01 | -3.38644687e-01 8.28353479e-01 -3.69337398e-01 3 5.64544266e-01 -7.97662125e-01 -1.87188236e-01 | 5.64544266e-01 -7.97662125e-01 -1.87188236e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FTF (Configuration in file "config-Cu-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -7.02081855453 2^p V(r_1,...,r_N) = -7.02081855453 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 8.28003294e-01 9.10900513e-01 1.09188629e+00 | 8.28003294e-01 9.10900513e-01 1.09188629e+00 1 6.23094794e-01 -5.68230822e-01 -6.53326607e-01 | 6.23094794e-01 -5.68230822e-01 -6.53326607e-01 2 -1.03498467e+00 5.22900052e-01 -6.43236893e-01 | -1.03498467e+00 5.22900052e-01 -6.43236893e-01 3 -4.16113418e-01 -8.65569743e-01 2.04677209e-01 | -4.16113418e-01 -8.65569743e-01 2.04677209e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Cu, PBC = FFT (Configuration in file "config-Cu-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -3.91685515827 2^p V(r_1,...,r_N) = -3.91685515827 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -6.37780874e+00 -6.91023973e+00 -4.43980008e+00 | -6.37780874e+00 -6.91023973e+00 -4.43980008e+00 1 1.03029452e+01 9.32295631e+00 -5.71818584e+00 | 1.03029452e+01 9.32295631e+00 -5.71818584e+00 2 1.83472378e+00 -4.18905391e+00 5.45121904e+00 | 1.83472378e+00 -4.18905391e+00 5.45121904e+00 3 -5.75986020e+00 1.77633733e+00 4.70676688e+00 | -5.75986020e+00 1.77633733e+00 4.70676688e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = TTT (Configuration in file "config-AgCu-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 1.53049865671 2^p V(r_1,...,r_N) = 1.53049865671 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -3.89720205e+00 -3.97257874e+00 -9.39413945e+00 | -3.89720205e+00 -3.97257874e+00 -9.39413945e+00 1 5.69695748e+00 2.10268584e+00 -5.07908558e+00 | 5.69695748e+00 2.10268584e+00 -5.07908558e+00 2 7.93408036e+00 -8.62781196e+00 6.89888882e+00 | 7.93408036e+00 -8.62781196e+00 6.89888882e+00 3 -9.73383579e+00 1.04977049e+01 7.57433622e+00 | -9.73383579e+00 1.04977049e+01 7.57433622e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = TTF (Configuration in file "config-AgCu-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.0568594723609 2^p V(r_1,...,r_N) = 0.0568594723609 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.51772048e+00 -5.39489643e+00 -4.15170929e+00 | -1.51772048e+00 -5.39489643e+00 -4.15170929e+00 1 1.24833239e+01 3.81184800e+00 -1.06309300e+01 | 1.24833239e+01 3.81184800e+00 -1.06309300e+01 2 1.36991047e+00 -4.15626093e+00 1.84170384e+00 | 1.36991047e+00 -4.15626093e+00 1.84170384e+00 3 -1.23355139e+01 5.73930936e+00 1.29409354e+01 | -1.23355139e+01 5.73930936e+00 1.29409354e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = TFT (Configuration in file "config-AgCu-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -4.38032800911 2^p V(r_1,...,r_N) = -4.38032800911 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.04839997e+00 -2.11209470e+00 -1.24210567e+00 | -1.04839997e+00 -2.11209470e+00 -1.24210567e+00 1 6.45740519e+00 2.87475025e+00 -6.83816513e+00 | 6.45740519e+00 2.87475025e+00 -6.83816513e+00 2 -2.81303341e-01 -2.81573886e+00 2.89246426e+00 | -2.81303341e-01 -2.81573886e+00 2.89246426e+00 3 -5.12770189e+00 2.05308331e+00 5.18780654e+00 | -5.12770189e+00 2.05308331e+00 5.18780654e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = TFF (Configuration in file "config-AgCu-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.596377155652 2^p V(r_1,...,r_N) = 0.596377155652 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -6.24288158e+00 -5.97545675e+00 -7.67944238e+00 | -6.24288158e+00 -5.97545675e+00 -7.67944238e+00 1 4.52839828e+00 2.36947815e+00 -6.16523167e+00 | 4.52839828e+00 2.36947815e+00 -6.16523167e+00 2 8.65369959e+00 -4.77553600e+00 4.41571115e+00 | 8.65369959e+00 -4.77553600e+00 4.41571115e+00 3 -6.93921629e+00 8.38151461e+00 9.42896290e+00 | -6.93921629e+00 8.38151461e+00 9.42896290e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = FTT (Configuration in file "config-AgCu-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.171922916903 2^p V(r_1,...,r_N) = -0.171922916903 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -2.42935839e+00 -2.44778163e+00 -5.35423417e+00 | -2.42935839e+00 -2.44778163e+00 -5.35423417e+00 1 7.07076234e+00 4.20485038e+00 -7.60118924e+00 | 7.07076234e+00 4.20485038e+00 -7.60118924e+00 2 5.76905939e+00 -1.35996872e+01 4.60732152e+00 | 5.76905939e+00 -1.35996872e+01 4.60732152e+00 3 -1.04104633e+01 1.18426185e+01 8.34810189e+00 | -1.04104633e+01 1.18426185e+01 8.34810189e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = FTF (Configuration in file "config-AgCu-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -2.11290583601 2^p V(r_1,...,r_N) = -2.11290583601 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -6.39363241e+00 -4.55315902e+00 -2.48402738e+00 | -6.39363241e+00 -4.55315902e+00 -2.48402738e+00 1 5.70689836e+00 7.59601736e+00 -5.75883943e+00 | 5.70689836e+00 7.59601736e+00 -5.75883943e+00 2 4.64884510e+00 -6.32916298e+00 6.80899046e+00 | 4.64884510e+00 -6.32916298e+00 6.80899046e+00 3 -3.96211105e+00 3.28630464e+00 1.43387635e+00 | -3.96211105e+00 3.28630464e+00 1.43387635e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag Cu, PBC = FFT (Configuration in file "config-AgCu-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -1.95603881564 2^p V(r_1,...,r_N) = -1.95603881564 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -4.72569243e+00 -5.70710910e+00 -2.07048789e+00 | -4.72569243e+00 -5.70710910e+00 -2.07048789e+00 1 8.38448080e+00 7.74466171e+00 -7.25736022e+00 | 8.38448080e+00 7.74466171e+00 -7.25736022e+00 2 4.60964940e+00 -7.53513459e+00 2.89868386e+00 | 4.60964940e+00 -7.53513459e+00 2.89868386e+00 3 -8.26843777e+00 5.49758198e+00 6.42916425e+00 | -8.26843777e+00 5.49758198e+00 6.42916425e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.